La razón, madre de la ciencia y el derecho modernos

The data from this study is reported and analyzed in this chapter. The researcher used the main focus of each research questions as topic headings in this chapter in order to maintain a logical sequence and organization; however, the research questions will be fully answered in Chapter 5 on Summary, Conclusions, and Recommendations. For the first research question, the researcher recognized that the state of Kansas has two levels of low performance for the reading, mathematics, and science assessments and these are ”unsatisfactory” and “basic”. The researcher also recognized that the unsatisfactory and basic scores could be added together to produce a third low achievement score: combined. Through correlational explorations the researcher sought to determine a stable score for low student performance.

Best Representation of Low Achievement

Research question 1: Of the three building rates for low achievement (unsatisfactory, basic and unsatisfactory + basic), which represented the most consistent measure in correlation with the building rates for low income?

Data were collected and analyzed for each of the three low achievement areas of reading, mathematics, and, science; thus, this research question applied to each of the three low

achievement areas. Table 4.1 reports the correlations between low income and low reading achievement for the seven subgroups of Kansas’s high schools. A first trend that was observed was that low income/unsatisfactory reading correlations closely paralleled those of the low income/combined score reading correlations. The mean correlation (r = 0.65) for unsatisfactory

Table 4.1 Low Income/Low reading Achievement Correlations Reported by High School Location and Size with Unsatisfactory, Basic, and Combined Reading Scores

Low Schools Unsatisfactory Basic Uns + bas Income n scores scores scores (comb.)

High school metropolitan location

Metro 1 22 0.80 0.70 0.79 Metro 2 19 0.58 0.44 0.61 Metro 3 28 0.83 0.61 0.83

High school size

6A sized 32 0.72 0.63 0.73 5A sized 30 0.79 0.56 0.78 4A sized 62 0.24 0.09 0.21 3A sized 59 0.56 0.40 0.59

Table 4.2 Low Income/Low Mathematics Correlations Reported by High School Location and Size with Unsatisfactory, Basic, and Combined Mathematics Scores

Low Schools Unsatisfactory Basic Uns + bas Income n scores scores scores (comb.)

High school metropolitan location

Metro 1 22 0.77 0.31 0.79 Metro 2 19 0.75 0.28 0.71 Metro 3 28 0.93 -0.12 0.89

High school size

6A sized 32 0.91 0.74 0.91 5A sized 30 0.88 -0.11 0.89 4A sized 62 0.19 0.27 0.27 3A sized 59 0.61 0.27 0.59

Table 4.3 Low Income/Low Science Achievement Correlations Reported by High School Location and Size with Unsatisfactory, Basic, and Combined Science Scores

Low Schools Unsatisfactory Basic Uns + bas

Income n scores scores scores (comb.)

High school metropolitan location

Metro 1 22 0.84 0.62 0.84 Metro 2 19 0.85 0.47 0.82

Metro 3 28 0.92 -0.06 0.90

High school size

6A sized 32 0.86 0.56 0.62 5A sized 30 0.89 0.04 0.91 4A sized 62 0.19 0.14 0.21 3A sized 59 0.57 0.61 0.69 Mean correl. 252 0.73 0.36 0.71

reading/low income was the same as the mean correlation (r = 0.65) for combined, unsatisfactory and basic reading/low income. The mean correlation (r = 0.49) for basic reading/low income was substantially lower than the other two. Thus, the researcher concluded that the most consistent low reading achievement/low income correlation was derived with the combined score of unsatisfactory + basic reading achievement.

Table 4.2 reports the correlations between low income and low mathematics achievement for the seven subgroups of Kansas high schools. A first trend that was observed was that the low income/unsatisfactory mathematics correlations paralleled those of low income/combined mathematics correlations. The mean correlation (r = 0.72) for unsatisfactory mathematics/low income was the same as the mean correlation (r = 0.72) for combined, unsatisfactory and basic mathematics/low income. The mean correlation (r = 0.30) for basic mathematics/low income was substantially lower than the other two. Thus, the researcher concluded that the most consistent low mathematics achievement/low income correlation was derived with the combined score of unsatisfactory + basic mathematics achievement.

Table 4.3 reports the correlations between low income and low science achievement for the seven subgroups of Kansas high schools. A first trend that was observed was that low income/unsatisfactory science correlations closely paralleled those of the low income/combined science correlations. The mean correlation (r = 0.73) for unsatisfactory science/low income was very close to the mean correlation (r = 0.71) for combined, unsatisfactory and basic science/low income. The mean correlation (r = 0.36) for basic science/low income was substantially lower than the other two. Thus, the researcher concluded that the most stable low science

achievement/low income correlation was derived with the combined score of unsatisfactory + basic science achievement. The trend in all three subject areas (reading, mathematics, and

science) was that the combined score (unsatisfactory + basic) proved to be the most consistent score in correlation to low income. As a result, when the researcher refers to low achievement in the remainder of this chapter, this is in reference to the combined scores (unsatisfactory + basic) in reading, mathematics, and science.

Observable Metropolitan Location Correlation Differences

Research question 2. What were the observable differences in the correlations (building rates of low income to low achievement) among the three metropolitan locations of high schools?

This research questions applied to each of the three low achievement areas of reading, mathematics, and science. Here the researcher identified the similarities and differences found in the data for the high schools in the three metropolitan locations and judged the magnitude of the correlations. Returning to Table 4.1, the main observable trend was that the low income/low reading correlation (r = 0.61) for metropolitan area 2 (Shawnee and adjacent counties) was observably lower than the correlation (r = 0.79) for metropolitan area 1 (Sedgwick County), and observably lower than the correlation (r = 0.83) for metropolitan area 3 (Wyandotte/Johnson and adjacent counties). For metropolitan area 1, the correlation was in the “high” category, and for metropolitan area 3, the correlation was in the “very high” range category while in metropolitan area 2 the correlation was in the “moderate” category.

Returning to table 4.2, the main observable trend was that the low income/low

mathematics achievement correlation (r = 0.71) for metropolitan area 2 (Shawnee and adjacent counties) was slightly lower than the correlation (r = 0.79) for metropolitan area 1 (Sedgwick County), and was observably lower than the correlation (r = 0.89) for metropolitan area 3 (Wyandotte/Johnson and adjacent counties). For metropolitan areas 1 and 2 the correlations were in the “high” category while metropolitan area 3 yielded a “very high” correlation.

Returning to table 4.3, the main observable trend was that the low income/low science achievement correlation (r = 0.82) for metropolitan area 2 (Shawnee and adjacent counties) was close to the correlation (0.84) for metropolitan area 1 (Sedgwick County), and was lower than the correlation (r = 0.90) for metropolitan area 3 (Wyandotte/Johnson and adjacent counties). For metropolitan areas 1, 2, and 3, all three correlations were in the “very high” category.

Observable High School Size Correlation Differences

Research question 3. What were the observable differences in the correlations (building rates for low income with building rates for low achievement) among the four different sizes of high schools?

This research question applied to each of the three low achievement areas of reading, mathematics, and science. Here the researcher identified the similarities and differences found in the data for the high schools in the four size categories and judged the magnitude of the

correlations. Returning to Table 4.1, the obvious trend was that 4A-sized high schools produced the lowest correlation (r = 0.21) for low income/low reading in comparison to the other three high school sizes (r = 0.73, 0.78, and 0.59). Further, the 6A-and 5A-sized correlations tended toward the “high” range. The correlation for the 3A-sized high schools was in the “moderate” range, while the 4A sized high school was clearly a “very low” correlation.

Returning to Table 4.2, the main trend was that 4A-sized high schools produced the lowest correlation (r = 0.27) for low income/low mathematics in comparison to the other three high school sizes (r = 0.91, 0.89, and 0.59). Further, the 6A-and 5A-sized correlations tended toward the “very high” range. The correlation for the 3A-sized high schools was in the “moderate range” while the 4A-sized high school score was clearly a “low” correlation.

Returning to Table 4.3, the obvious trend was that the 4A-sized high schools produced the lowest correlation (r = 0.21) for low income/low science in comparison to the other three high schools (r = 0.62, 0.91, 0.69, respectively). Furthermore, the 6A-sized correlations were in the “moderate” range and the 3A-sized correlations tended toward the “moderate to high” range. The correlation for the 5A-sized high schools was in the “very high” range, while the 4A-sized high school score was clearly a “very low” correlation.

Low Income/Low Achievement Correlation Differences

Research question 4. What were the observable differences in the correlations (building rates for low income with building rates for low achievement) when the subjects of reading, mathematics and science were considered?

Table 4.4 summarizes the low income/low achievement correlations by reading, mathematics, and science for metropolitan high school location. These data were taken from Tables 4.1, 4.2, and 4.3 for each of the three metropolitan locations and reported in ranked order of highest, second highest, and third highest correlations. Table 4.5 summarizes the low

income/low achievement correlations by reading, mathematics, and science for high school size. These data were taken from Tables 4.1, 4.2, and 4.3 for each of the high school size groups and reported in ranked order by the highest, second highest, and third highest correlations.

The observable differences in the correlations (building rates for low income with building rates for low achievement) when considering the subjects of reading, mathematics, and science for the total high schools without regard to metropolitan location or school size are as follows: The highest correlations were found in low science achievement and low mathematics achievement only. Low science achievement has the highest correlations in all three

Table 4.4 Summary of Correlations: Low Income with Low Reading Achievement, Low Mathematics Achievement, Low Science Achievement Reported by High School Metropolitan Location

Group r

Metropolitan area 1

Low science achievement 0.84 Low reading achievement 0.79 Low mathematics achievement 0.79

Metropolitan area 2

Low science achievement 0.82 Low mathematics achievement 0.71

Low reading achievement 0.61

Metropolitan area 3

Low science achievement 0.90 Low mathematics achievement 0.89

Table 4.5 Summary of Correlations: Low Income with Low Reading Achievement, Low Mathematics Achievement, and Low Science Achievement Reported by High School Size

Group r

6A high schools

Low mathematics achievement 0.91 Low reading achievement 0.73 Low science achievement 0.62

5A high schools

Low science achievement 0.91 Low mathematics achievement 0.89

Low reading achievement 0.78

4A high schools

Low mathematics achievement 0.27 Low reading achievement 0.21

Low science achievement 0.21

3A high schools

Low science achievement 0.69 Low reading achievement 0.59 Low mathematics achievement 0.59

metropolitan locations (r = 0.84, r = 0.82, and r = 0.90) and in the 5A (r = 0.91) and 3A (r = 0.69) high schools. Low mathematics achievement has the highest correlations in the 6A (r = 0.91) and 4A (r = 0.27) high schools. The second highest correlations were found in low reading

achievement and low mathematics achievement only. Low reading achievement has the second highest correlations in metropolitan location 1(r = 0.79), the 6A (r = 0.73), 4A (r = 0.21), and 3A (r = 0.59) high schools. Low mathematics achievement has the second highest correlations in metropolitan location 2 (r = 0.71), metropolitan 3 (r = 0.89) and in the 5A (r = 0.89) high schools. The third highest correlations were found in low reading achievement, low mathematics and low science achievement. Low mathematics achievement has the third highest correlations in metropolitan location 1(r = 0.79) and the 3A (r = 0.59) high schools. Low reading achievement has the third highest correlations in metropolitan location 2 (r = 0.61), metropolitan location 3 (r = 0.83), and the 5A (r = 0.78) high schools. Low science achievement has the third highest correlations in the 6A (r = 0.62) and 4A (r = 0.21) high schools.

Description Statistic Inferences

Research question 5. What did the analysis of standard deviation scores, range scores, and frequency distributions reveal about differences in correlations (building rates for low income with building rates for low achievement) for high school metropolitan location and high school size.

Standard deviation scores. Table 4.6 summarizes the standard deviation scores for low

income, low reading achievement, low mathematics achievement, and low science achievement. The reader is reminded that the low achievement scores were those derived by adding the unsatisfactory scores to the basic scores. The data in Table 4.6 is reported by the metropolitan

Table 4.6 Standard Deviation Scores for Percent Low Income and Percent Low

Achievement (Reading, Mathematics, and Science) Reported by High School Metropolitan Location and High School Size

Group % Low % Low % Low % Low

Income Reading Math Science

High school metropolitan location

Metro 1 23.59 15.46 18.05 24.31 Metro 2 12.95 12.38 14.37 13.46 Metro 3 23.46 17.33 20.15 21.07

High school size

6A 18.52 11.10 14.61 15.26 5A 22.27 15.73 17.60 20.87 4A 09.76 09.74 10.81 10.51 3A 13.61 13.49 17.32 17.59

Table 4.7 Range Scores for Percent Low Income, Low Reading Achievement, Low

Mathematics Achievement and Low Science Achievement Reported for Metropolitan High School Location

Group %Low %Low %Low %Low Income Reading Math Science

Metro1 Min/max 0.0-86.49 18.20-73.90 31.90-95.50 16.40-95.20 Range 86.49 55.70 63.60 78.80 Metro 2 Min/max 11.68-65.97 27.70-71.00 26.70-87.90 13.30-80.10 Range 54.29 43.30 61.20 66.80 Metro3 Min/max 0.96-82.24 18.70-80.80 26.40-97.00 22.90-95.70 Range 81.28 62.10 70.60 72.80

Table 4.8 Range Scores for Percent Low Income, Low Reading Achievement, Low Mathematics Achievement and Low Science Achievement Reported for High School Size

Group %Low %Low %Low %Low Income Reading Math Science 6A sized Min/max 0.96-65.60 18.70-56.10 26.40-75.10 22.90-71.40 Range 64.60 37.40 48.70 48.50 5A sized Min/max 0.0-82.24 18.20-80.60 35.40-97.00 18.70-95.70 Range 82.24 62.40 61.60 77.00 4A sized Min/max 4.15-46.33 14.30-60.80 32.40-71.00 20.30-69.20 Range 42.18 46.50 38.60 48.90 3A sized Min/max 0.0-86.49 7.10-73.90 16.0-95.50 13.30-95.20 Range 86.49 66.80 79.50 81.90

locations and by the four high school size groups. In the case of high school metropolitan location, the standard deviation scores (low income, low reading, low mathematics, and low science) for the high schools in metropolitan area 2 were smaller than those for metropolitan areas 1 and 3. These smaller metropolitan area 2 standard deviations reflect narrower

distributions of scores, and these narrower distributions could have contributed to smaller low income/low achievement correlations reported previously for metropolitan area 2.

Table 4.6 also shows that the standard deviation scores (low income, low reading, low mathematics, and low science) for 4A-sized high schools were smaller than those of the 6A-,5A- ,and 3A-sized high schools. The smaller 4A sized high school standard deviations reflect the narrower distributions of scores, and these narrower distributions could have contributed to smaller low income/low achievement correlations reported previously for 4A-sized high schools.

Range scores. Table 4.7 summarizes the range scores for low income, low reading

achievement, low mathematics achievement, and low science achievement. The data in Table 4.7 is reported by the high schools in the three metropolitan locations. The low achievement scores were those derived by adding the unsatisfactory scores to the basic scores. The trend shown in Table 4.7 was that the range scores for high schools in metropolitan area 2 were smaller than those in metropolitan areas 1 and 3. This reinforces the trend shown by the previously reported standard deviation scores that showed that metropolitan area 2 produced narrower distributions.

Table 4.8 summarizes the range scores for low income, low reading achievement, low mathematics achievement, and low science achievement. The data in Table 4.8 is reported by the high schools in the four school size categories. The low achievement scores were those derived by adding the unsatisfactory scores to the basic scores. The trend shown in Table 4.8 was

that the range scores for 4A-sized high schools were smaller than those for 6A-, 5A-, and 3A- sized high schools. This reinforces the trend shown by the previously reported standard deviation scores that shows that 4A-sized high schools produced narrower distributions. At the same time, the researcher found two exceptions to the trend of lower range scores for 4A-sized high schools. The 6A-sized high schools produced smaller range scores in comparison to 4A-sized high schools in low reading achievement (6A range = 37.40, 4A range = 46.50). The 6A-sized high schools also produced smaller range scores in comparison to 4A-sized high schools in low science achievement (6A range = 48.50, 4A range = 48.90).

Frequency distributions. Here the researcher continued his examination of descriptive

statistics in order to better understand the trends in the low income/low achievement correlations reported at the beginning of this chapter. The researcher established ten-point frequency intervals for percentages of low income, low reading achievement, low mathematics achievement, and low science achievement. The frequency distributions reflect the number and percent of high schools in each interval. The data are reported first, by high school location (Tables 4.9, 4.10, 4.11, 4.12), and second, by high school size (Tables 4.13, 4.14, 4.15, and 4.16). The low achievement scores in the intervals were those derived by adding the basic scores to the unsatisfactory scores.

Table 4.9. Frequencies in the percent of low-income students for high schools by metropolitan location. The three metropolitan locations have sizeable cumulative percentages of

high schools in the percentage of low-income students in the intervals of 0-30, and the data below were taken from table 4.9 to illustrate this.

Metro area Cumulative % low-income students per high schools 1 54.55 (intervals 0-30)

Table 4.9 Frequencies in the Percent of Low-Income Students for High Schools by Metropolitan Location (n=69 High Schools)

School Location

Intervals Metro 1 Metro 2 Metro 3 f % f % f % 0 - 10 03 13.64 00 00.00 16 57.14 11 - 20 06 27.27 11 57.89 05 17.86 21 - 30 03 13.64 05 26.32 02 07.14 31 - 40 02 09.09 01 05.26 00 00.00 41 - 50 03 13.64 01 05.26 01 03.57 51 - 60 02 09.09 00 00.00 01 03.57 61 - 70 02 09.09 01 05.26 01 03.57 71 - 80 00 00.00 00 00.00 01 03.57 81 - 90 01 04.55 00 00.00 01 03.57 91 - 100 00 00.00 00 00.00 00 00.00 Totals 22 100.00 19 100.00 28 100.00

2 84.21 (intervals 0-30) 3 82.14 (intervals 0-30) Beyond the intervals of 0-30, Table 4.9 shows that metropolitan area 1 has a continuous distribution of high schools throughout the higher percentage frequencies of low-income students. This is true for metropolitan area 3. In contrast to metropolitan areas 1 and 3,

metropolitan area 2 has only one high school in the interval of 61-70 and none in intervals of 71- 100.

Table 4.10. Frequencies in the percent of low reading achievement students for high schools by metropolitan location. Cumulative frequencies in low reading-achievement

students (intervals 11-50) in the three metropolitan areas have been taken from Table 4.10 and are illustrated as follows:

Metro area Cumulative % low reading achievement students per high schools 1 68.18 (intervals 11-50) 2 84.21 (intervals 11-50) 3 71.43 (intervals 11-50)

Metropolitan area 2 high schools have the greatest cumulative percent (84.21%) of low reading- achievement students in high schools in the interval range of 11-50. Metropolitan area 1 has a bimodal distribution (Table 4.10) and includes high schools in the higher intervals of low reading achievement students. Metropolitan area 3 has a continued distribution beyond the interval range of 11-50.

Table 4.10 Frequencies in the Percent of Low Reading Achievement Students for High Schools by Metropolitan Location (n=69 High Schools)

School Location

Intervals Metro 1 Metro 2 Metro 3

f % f % f % 0 - 10 00 00.00 00 00.00 00 00.00 11 - 20 02 09.09 01 05.26 01 03.57 21 - 30 04 18.18 03 15.79 09 32.14 31 - 40 08 36.36 07 36.84 07 25.00 41 - 50 01 04.55 05 26.32 03 10.71 51 - 60 05 22.73 02 10.53 04 14.29 61 - 70 01 04.55 01 05.26 01 03.57 71 - 80 01 04.55 00 00.00 03 10.71 81 - 90 00 00.00 00 00.00 00 00.00 91 - 100 00 00.00 00 00.00 00 00.00 Totals 22 100.00 19 100.00 28 100.00

Table 4.11. Frequencies in the percent of low mathematics achievement students for high schools by metropolitan location. Cumulative frequencies in percentages of low

mathematics achievement students in the three metropolitan area high schools have been taken from Table 4.11 and are illustrated as follows.

Metro area Cumulative % low math achievement students per high schools 1 68.18 (intervals 31-70)

2 89.47 (intervals 31-70) 3 75.00 (intervals 31-70)

Here the pattern is clear in that metropolitan area 2 has its cumulative frequency of percentage of low mathematics achievement students (89.47%) concentrated across four intervals while the other two metropolitan areas have lower cumulative frequencies (68.18%, 75.00%) across the same four intervals.

Table 4.11 Frequencies in the Percent of Low Mathematics Achievement Students for High Schools by Metropolitan Location (n=69 High Schools)

School Location

Intervals Metro 1 Metro 2 Metro 3 f % f % f % 0 - 10 00 00.00 00 00.00 00 00.00 11 - 20 00 00.00 00 00.00 00 00.00 21 - 30 00 00.00 01 05.26 01 03.57 31 - 40 04 18.18 02 10.53 09 32.14 41 - 50 03 13.64 08 42.11 07 26.15 51 - 60 05 22.73 02 10.53 01 03.57 61 - 70 03 13.64 05 26.71 04 14.29 71 - 80 04 18.18 00 00.00 02 07.14 81 - 90 02 09.09 01 05.26 01 03.57 91 - 100 01 04.55 00 00.00 03 10.71 Totals 22 100.00 19 100.00 28 100.00

Table 4.12. Frequencies in the percent of low science achievement students for high schools by metropolitan location. Cumulative frequencies in the percentage of low science

achievement students in the three metropolitan area high schools have been taken from Table 4.12 and are illustrated as follows:

Metro area Cumulative % low science achievement students per high schools 1 50.00 (intervals 31-70)

2 89.47 (intervals 31-70) 3 67.86 (intervals 31-70)

Here the pattern is clear in that metropolitan area 1 has 50.00% of low science achievement students in high schools systemically distributed across four intervals. In contrast, metropolitan area 2 has 89.47% of low science achievement students in high schools concentrated in four intervals and metropolitan area 3 has 67.86 % of low science achievement in high schools distributed across the same four intervals.

Table 4.12 Frequencies in the Percent of Low Science Achievement Students for High Schools by Metropolitan Location (n=69 High Schools)

In document Ciencia y proceso: la prueba del ADN en el proceso penal español (página 30-35)